In that program, the editor is able to use two source monitors to mark clips from the scene coverage. Is there a similar feature in Avid? If not, what is the best way of switching between shots in Avid when assembling a dialog edit like this?

Media Composer has had pop-up monitors since v1 in 1989. Option-double/Alt click source clip and it will becomes its own viewer/monitor. You can have as many as you want. You can drag other clips into those if you only want to have a set number of them available. I have also ganged different takes together when performances are close (faux multicam). But for scripted dialog editing, nothing really beats using ScriptSync. http://www.avid.com/US/products/scriptsync

Even if you don't purchase the automated syncing, you can still align takes to the script as needed and sync manually. May not be beneficial for a lot of scenes, but for the more complex ones with lots of coverage, it is fantastic.